Krishna
1

Step 1:  Draw a figure from the given information.

                


              GIVEN:  Height of the pole AB = 10 m

                            Angle between the rope and pole  \angle CAB\ =\ 30\degree

                              Length of the rope AC = ?


Step 2: Determine the length of the rope by using the trigonometric ratios.

            EXAMPLE:  We need to find the rope length(hypotenuse)

                                  So,  take \cos A = \frac{adjacent}{hypotenuse}


                                                  \cos 30\degree = \frac{AB}{AC} = \frac{10}{AC}


                                                    \frac{\sqrt{3}}{2} = \frac{10}{AC}   (Since \cos 30\degree = \frac{\sqrt{3}}{2})


                                                    AC = \frac{2*10}{\sqrt{3}}

                                                        Simplify

                                                  AC = \frac{20}{\sqrt{3}} \frac{\sqrt{3}}{\sqrt{3}} ( \because Rationalization)


                                                AC = \frac{20\sqrt{3}}{3}


                                                AC = \frac{20 * 1.732}{3} ( \because \sqrt{3} = 1.732 )


                                               AC = 11.55 m


                                   Length of the rope = 11.55 m